Reflection suppression element and optical apparatus

ABSTRACT

The optical element includes a base member, and a first layer which is formed on the base member and whose refractive index for a central use wavelength λ changes in a thickness direction of the first layer by 0.05 or more. The first layer has an anti-reflection function and satisfies n t =n i+0.1(n   s −n i ), 0.5≦[n{t(n t )/2}−n t ]/[n s −n{t(n t )/2}]≦0.8, λ/4≦t(n t )≦2λ and 1.0≦n i≦1.1. n   i  represents a refractive index of a most light entrance side part of the first layer for the central use wavelength, n s  represents a refractive index of a most base member side part of the first layer for the central use wavelength, t(n t ) represents an optical film thickness of the first layer at which the refractive index thereof for the central use wavelength is n t , and n{t(n t )/2} represents a refractive index of the first layer for the central use wavelength at a position where the optical film thickness ism t(n t )/2.

BACKGROUND OF THE INVENTION

The present invention relates to an optical element provided with astructure having a reflection suppressing effect (anti-reflectionfunction), and to an optical apparatus including the optical element.

In general, on at least one surface of an optical element formed of atransparent member, a thin film having an anti-reflection function isformed by using a film forming method typified by vapor deposition andsputtering. However, such a film forming method limits materials thatcan be used for film formation, which makes it difficult to obtain athin film having an arbitrary refractive index.

Japanese Examined patent publication No. 61-51283 discloses a method forvirtually obtaining a thin film having an intermediate refractive indexby selectively introducing a thin film having a high refractive indexand a thin film having a low refractive index and by appropriatelysetting thicknesses of the introduced thin films.

Further, another method forms an anti-reflection structure constitutedby plural structure portions (protrusions) each smaller than a usewavelength (that is, a wavelength of light entering the optical element)on at least one surface of an optical element. The most famousanti-reflection structure is a moth-eye structure. A surface of themoth-eye structure provides a very low reflectance due to amicrostructure unique to the moth-eye structure.

In a microstructure whose each structure portion is smaller than the usewavelength, light of the use wavelength cannot recognize themicrostructure and therefore behaves as if entering a uniform medium.The microstructure has a refractive index according to a volume ratio ofa material forming the microstructure. The use of this can realize amicrostructure having a low refractive index that cannot be obtained byusing normal materials. The use of such a low refractive indexmicrostructure can achieve a higher performance anti-reflectionfunction.

Japanese Patent Laid-Open No. 2005-62674 discloses an anti-reflectionstructure formed by the above-described microstructure in whichprotrusions have a tapered shape toward a surface side (light entranceside). In such an anti-reflection structure, a refractive indexgradually reduces from a base member side of an optical element towardthe surface side thereof.

Japanese Patent Laid-Open No. 2003-240904 discloses a microstructureconstituted by plural protrusions each having a shape in which, incomparison of a most convex portion and a most concave portion of theprotrusion, the most convex portion is sharper than the most concaveportion. Such a shape of the protrusion makes change in refractive indexat a superficial surface part or a boundary part between themicrostructure and the base member more gently, which reduces thereflectance of the microstructure.

However, the film virtually having the intermediate refractive indexdisclosed in Japanese Examined patent publication No. 61-51283 isinferior in a broadband characteristic since the film is formed by usinga high refractive index material.

Japanese Patent Laid-Open No. 2005-62674 does not disclose an optimalrefractive index structure though it discloses a microstructure formedso as to be tapered in order to gradually change the refractive index.

Further, the microstructure disclosed in Japanese Patent Laid-Open No.2003-240904 is focused only on the change of the refractive index at aboundary surface, which generates part where the refractive indexgreatly changes, and therefore a good broadband characteristic cannot beobtained.

Thus, the film disclosed in Japanese Examined patent publication No.61-51283 and the microstructures disclosed in Japanese Patent Laid-OpenNo. 2005-62674 and Japanese Patent Laid-Open No. 2003-240904 can realizean anti-reflection function under restricted conditions. However, theanti-reflection function is inferior in the broadband characteristic aswell as in an incident angle characteristic.

SUMMARY OF THE INVENTION

The present invention provides an optical element having a reflectionsuppressing function (anti-reflection function) excellent in a broadbandcharacteristic and an incident angle characteristic, and an opticalapparatus including the optical element.

The present invention provides as one aspect thereof an optical elementincluding a base member, and a first layer which is formed on the basemember and whose refractive index for a central use wavelength λ changesin a direction of a thickness of the first layer by 0.05 or more. Thefirst layer has an anti-reflection function and satisfies the followingconditions:

n_(t) = n_(i) + 0.1 ⋅ (n_(s) − n_(i))$0.5 \leq \frac{{n\left\{ {{t\left( n_{t} \right)}/2} \right\}} - n_{t}}{n_{s} - {n\left\{ {{t\left( n_{t} \right)}/2} \right\}}} \leq 0.8$$\frac{\lambda}{4} \leq {t\left( n_{t} \right)} \leq {2\;\lambda}$1.0 ≤ n_(i) ≤ 1.1

where n_(i) represents a refractive index of a most light entrance sidepart of the first layer for the central use wavelength, n_(s) representsa refractive index of a most base member side part of the first layerfor the central use wavelength, t(n_(t)) represents an optical filmthickness of the first layer at which the refractive index thereof forthe central use wavelength is n_(t), and n{t(n_(t))/2} represents arefractive index of the first layer for the central use wavelength at aposition where the optical film thickness is t(n_(t))/2.

The present invention provides as another aspect thereof an opticalapparatus including the above-described optical element.

Other aspects of the present invention will become apparent from thefollowing description and the attached drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a refractive index structure of a graded layer in eachembodiment of the present invention.

FIG. 2 shows a basic structure of an optical element of each embodiment.

FIG. 3 shows a structure of an optical element in which a layer having auniform refractive index is formed on a base member.

FIG. 4 shows a refractive index structure in a case where the uniformrefractive index layer is formed on the base member.

FIG. 5 shows a refractive index structure of a graded layer whoserefractive index changes uniformly with respect to an optical filmthickness.

FIG. 6 shows a reflectance characteristic in a case where the gradedlayer shown in FIG. 5 is added to a base member.

FIG. 7 shows a reflectance characteristic in a case where the gradedlayer shown in FIG. 1 is added to a base member.

FIG. 8 shows a structure of an optical element in a case where a gradedlayer is formed as a microstructure layer in each embodiment.

FIG. 9 shows a refractive index structure of a graded layer ofEmbodiment 1.

FIG. 10 shows a reflectance characteristic of Embodiment 1.

FIG. 11 shows a refractive index structure of a graded layer ofEmbodiment 2.

FIG. 12 shows a refractive index structure of an optical element ofEmbodiment 2.

FIG. 13 shows a reflectance characteristic of Embodiment 2.

FIG. 14 shows a refractive index structure of a graded layer ofEmbodiment 3.

FIG. 15 shows a refractive index structure of an optical element ofEmbodiment 3.

FIG. 16 shows a reflectance characteristic of Embodiment 3.

FIG. 17 shows a refractive index structure of a graded layer ofEmbodiment 4.

FIG. 18 shows a reflectance characteristic of Embodiment 4.

FIG. 19 shows a refractive index structure of a graded layer ofComparative Example 1.

FIG. 20 shows a reflectance characteristic of Comparative Example 1.

FIG. 21 shows a refractive index structure of a graded layer ofComparative Example 2.

FIG. 22 shows a reflectance characteristic of Comparative example 2.

FIG. 23 schematically shows a digital camera using the optical elementof each embodiment.

FIG. 24 shows a refractive index structure of a graded layer ofEmbodiment 5.

FIG. 25 shows a reflectance characteristic of Embodiment 5.

FIG. 26 shows a refractive index structure of a graded layer ofEmbodiment 6.

FIG. 27 shows a reflectance characteristic of Embodiment 6.

FIG. 28 shows a refractive index structure of a graded layer ofComparative Example 3.

FIG. 29 shows a reflectance characteristic of Comparative Example 3.

DESCRIPTION OF THE EMBODIMENTS

Exemplary embodiments of the present invention will be describedhereinafter with reference to the accompanying drawings.

First, description will be made of common matters to embodiments(Embodiments 1 to 6) described below before specific descriptionthereof.

Each embodiment describes an example in which a use wavelength range is400 to 700 nm or 300 to 1000 nm and a central wavelength thereof(hereinafter referred to as central use wavelength) is 550 nm or 650 nm.However, the use wavelength range and the central use wavelength are notlimited to the above wavelength range and wavelength, and may be otherwavelength range and wavelength.

FIG. 2 shows a basic configuration common to optical elements ofEmbodiment 1 to 6. Reference numeral 021 denotes a-first layer, which ishereinafter referred to as “graded layer”. The graded layer means alayer whose refractive index changes in a z-direction that is athickness direction of the layer (also referred to as “layer thicknessdirection” or “film thickness direction”). The graded layer 021 has areflection suppressing function (in other words, an anti-reflectionfunction).

Reference numeral 022 denotes a base member (base material) whichcorresponds to a main body (transmissive member) of the optical elementincluding the graded layer 021. FIG. 2 shows a case where the gradedlayer 021 is formed on one surface of the base member 022. However, thegraded layer 021 may be formed on both surfaces of the base member 022(in other words, it is only necessary that the graded layer be formed onat least one surface of the base member).

Reference numeral 023 schematically shows a refractive index structureof the graded layer 021. A horizontal axis shows refractive index n ofthe graded layer 021, and a vertical axis shows optical film thickness tof the graded layer 021.

FIG. 1 shows the above-mentioned refractive index structure 023 in moredetail. However, the refractive index structure shown in the FIG. 1 isrotated by 90 degrees with respect to that shown in FIG. 2. A horizontalaxis in the FIG. 1 shows the optical film thickness t and a verticalaxis therein shows the refractive index n. A solid line 011 shows changeof the refractive index of the graded layer 021 with respect to theoptical film thickness. In the horizontal axis showing the optical filmthickness t, an origin O denotes a boundary surface between the basemember 022 and the graded layer 021, and t_(i) represents a totaloptical film thickness of the graded layer 021.

When viewed from a base member side, the refractive index n of thegraded layer 021 changes from n_(s) to n_(i). n_(i) represents arefractive index of a most surface side part (that is, a mostsuperficial surface) of the graded layer 021 for the central usewavelength. The most surface side part of the graded layer 021 can bealso said as a most light entrance side part. Moreover, n_(s) representsa refractive index of a most base member side part of the graded layer021 for the central use wavelength.

The refractive index of the graded layer 021 changes more gently in thelight entrance side part thereof than in the base member side partthereof. This is the same in FIGS. 9, 11, 14, 17, 24 and 26 used later.

Each embodiment defines n_(t) by using n_(s) and n_(i). n_(t) is shownby the following expression (1).n _(t) =n _(i)+0.1·(n _(s) −n _(i))  (1)

Each embodiment satisfies a condition shown by the following expression(2):

$\begin{matrix}{0.5 \leq \frac{{n\left\{ {{t\left( n_{t} \right)}/2} \right\}} - n_{t}}{n_{s} - {n\left\{ {{t\left( n_{t} \right)}/2} \right\}}} \leq 0.8} & (2)\end{matrix}$where t(n_(t)) represents an optical film thickness of the graded layer021 at which the refractive index thereof for the central use wavelengthis n_(t), and n{t(n_(t))/2} represents a refractive index of the gradedlayer 021 for the central use wavelength at a position where the opticalfilm thickness is t(n_(t))/2.

The condition shown by the expression (2) relates to a degree of thechange of the refractive index of the graded layer 021 from a part(position) where the optical film thickness is t(n_(t)) to apart(position) where the optical film thickness is t(n_(t))/2.

The anti-reflection function can be explained by interference of lightwaves. This is the same in the graded layer whose refractive indexchanges thereinside in its thickness direction. In the explanation bythe light wave interference, a change amount of the refractive indexshows an amplitude of the light wave, and the optical film thicknessshows a phase difference amount of the light waves.

FIG. 3 shows an example of a layer having a uniform refractive index inthe thickness direction. Reference numeral 032 denotes a base member,and reference numeral 031 denotes a thin film layer having a uniformrefractive index in the thickness direction. Reference numeral 033schematically shows a refractive index structure of the thin film layer031.

FIG. 4 shows the above-mentioned refractive index structure 033 in moredetail. However, the refractive index structure shown in the FIG. 4 isrotated by 90 degrees with respect to that shown in FIG. 3. A horizontalaxis in FIG. 4 shows optical film thickness t and a vertical axistherein shows refractive index n. Reference numeral 041 denotes arefractive index and an optical film thickness of the thin film layer031.

Reference numeral 042 shows a light wave reflected at a surface of thethin film layer 031, and reference numeral 043 shows a light wavereflected at a boundary surface between the thin film layer 031 and thebase member 032. FIG. 4 shows interference of the light waves 042 and043 when the optical film thickness t_(s) of the thin film layer 031 isλ/4. In this case, the light waves 042 and 043 have a phase differenceamount of about λ/2, thereby negating each other. As a result, the thinfilm layer 031 functions as an anti-reflection film.

On the other hand, FIG. 5 shows an example of a refractive indexstructure of an optical element having a graded layer. FIG. 5 shows acase where the refractive index uniformly changes with respect to theoptical film thickness. Reference numeral 051 denotes the change of therefractive index with respect to the optical film thickness. Referencenumeral 052 denotes part of light waves (reflected waves) reflected atrespective positions on the graded layer.

Although the graded layer shown in FIG. 5 does not include a clearboundary surface, the light waves are reflected at respective partswhere the refractive index changes. In other words, innumerable lightsare reflected in the graded layer shown in FIG. 5, and the reflectedwaves 052 shown in FIG. 5 are part of the innumerable lights. Ananti-reflection characteristic of such a graded layer is obtained bysuperposition of all reflected waves 052 from the respective opticalfilm thicknesses.

Each embodiment makes it a condition that a difference between n_(s) andn_(i) is 0.05 or more, in other words, the refractive index of thegraded layer for the central use wavelength changes by 0.05 or more inthe thickness direction. This is a condition for providing theanti-reflection characteristic by the interference of the light waves inthe graded layer.

Further, this condition also means that the refractive index greatlychanges in the graded layer. The great change of the refractive indexprovides a great influence on a reflectance characteristic. Therefore,each embodiment is characterized by satisfying the conditions shown bythe expressions (1) and (2).

In the expression (1), n_(t) shows a value between the refractiveindexes n_(s) and n_(i). The expression (2) shows a gradient of therefractive index between n_(t) and n_(s). The expression (2) means thatthe change of the refractive index (n_(s)−n{t(n_(t))/2}) in a basemember side part of the graded layer more inside than a surface sidepart thereof provides a greater influence on the light wave interferencethan the change of the refractive index (n{t(n_(t))/2}−n_(t)) in thesurface side part.

Moreover each embodiment is characterized in that the optical filmthickness t(n_(t)) of the graded layer for the central use wavelength λsatisfies a condition shown by the following expression (3):

$\begin{matrix}{\frac{\lambda}{4} \leq {t\left( n_{t} \right)} \leq {2\;\lambda}} & (3)\end{matrix}$

The optical film thickness t(n_(t)) of the graded layer smaller than λ/4does not cause sufficient light wave interference in the graded layer,so that the graded layer cannot function as an anti-reflection film. Onthe other hand, the optical film thickness t(n_(t)) larger than 2λ makesit very difficult to form the graded layer shown in FIG. 5.

It is more preferable that the range of the expression (3) be a rangefrom λ/3 to 3λ/2 (λ/3 or more and 3λ/2 or less). It is still morepreferable that the range of the expression (3) be a range from 3λ/8 to5λ/4 (3λ/8 or more and 5λ/4 or less).

Furthermore, each embodiment is characterized by satisfying a conditionshown by the following expression (4):1.0≦n _(i)≦1.1  (4)

When n_(i) exceeds the upper limit of the expression (4), a differencebetween a refractive index of a tip end of the graded layer shown inFIG. 5 and that of air becomes large, and thereby light reflected at aboundary surface of the graded layer and the air increases. Therefore,it becomes difficult to reduce the reflectance in the entire wavelengthrange.

FIG. 6 shows an example of a reflectance characteristic in a case wherethe graded layer shown in FIG. 5 is added to the base member. Ahorizontal axis shows wavelength λ and a vertical axis shows reflectanceR. Reference numeral 061 denotes a reflectance characteristic of onlythe base member, and reference numeral 062 denotes the reflectancecharacteristic in the case where the graded layer shown in FIG. 5 isadded to the base member. The refractive index of the base member isn_(s).

In the case shown in FIG. 6, the value of the expression (2) for thegraded layer shown in FIG. 5 is 1.0, which does not satisfy thecondition shown by the expression (2). In this reflectancecharacteristic, while the reflectance for a specific wavelength isalmost 0, the reflectance in other wavelengths is increased.

On the other hand, FIG. 7 shows a reflectance characteristic in a casewhere the graded layer 021 shown in FIG. 2 is added to the base member.A horizontal axis shows wavelength λ and a vertical axis showsreflectance R. Reference numeral 071 denotes a reflectancecharacteristic of only the base member, and reference numeral 072denotes the reflectance characteristic in the case where the gradedlayer 021 is added to the base member. The refractive index of the basemember is n_(s).

In the case shown in FIG. 7, the value of the expression (2) for thegraded layer 021 is 0.52, which satisfies the condition shown by theexpression (2). The reflectance characteristic in this case has twominimum values, which shows that an extremely low reflectance isachieved in a broad wavelength range as compared with the reflectancecharacteristic shown in FIG. 6.

The satisfaction of the conditions shown by the expressions (1), (2),(3) and (4) enables acquisition of reflection suppressing performance(anti-reflection performance) with an excellent broadbandcharacteristic.

On the other hand, when the value of the expression (2) is smaller than0.5, the change of the refractive index in the base member side part ofthe graded layer further than the surface side part whose refractiveindex is low becomes large, which makes it difficult to reduce thereflectance. Further, it is difficult to obtain a W-letter shapedreflectance characteristic, so that the broadband characteristic isdeteriorated. In addition, when the value of the expression (2) is 0.8or more, the refractive index changes nearly linearly with respect tothe optical film thickness, and therefore the broadband characteristicis deteriorated.

It is more preferable that the range of the value of the expression (2)be a range from 0.55 to 0.75 (0.55 or more and 0.75 or less). It isstill more preferable that the range of the value of the expression (2)be a range from 0.58 to 0.7 (0.58 or more and 0.7 or less).

In order to add a high performance anti-reflection function to variousglass materials having mutually different refractive indexes, it isnecessary to adjust the refractive index of the graded layer so as toadapt it to the respective glass materials. Thus, in each embodiment, itis preferable to provide at least one optical interference layer betweenthe base member that is a glass material and the graded layer to form alaminated structure by using the graded layer and the opticalinterference layer.

Adjusting a refractive index and a film thickness of the opticalinterference layer in such a laminated structure can realize a highperformance anti-reflection laminated structure usable for various glassmaterials, without adjusting the refractive index of the graded layer.

Moreover, it is preferable that a refractive index of at least one ofthe above-described optical interference layer for the central usewavelength λ be a refractive index between the refractive index of thebase member and n_(s). This can realize a refractive index structure inwhich the refractive index gradually decreases from the base member tothe most superficial surface of the graded layer. Such a refractiveindex structure prevents increase of light reflection caused due tooblique incidence of light, which makes it possible to obtain ananti-reflection laminated structure excellent in the broadbandcharacteristic and an oblique incidence characteristic.

Furthermore, in each embodiment, it is preferable to form the gradedlayer into a microstructure layer constituted by plural structureportions each smaller than the central use wavelength λ. FIG. 8 shows anexample of a structure in which such a microstructure layer is formed onthe base member. Reference numeral 081 denotes the microstructure layer(graded layer), and reference numeral 082 denotes the base member.

In a microstructure whose each structure portion is sufficiently smallerthan the central use wavelength λ, as described before, light enteringthe microstructure cannot recognize the microstructure itself andtherefore behaves as if entering a homogeneous medium. In this case, theentering light shows a characteristic as if the microstructure isaveraged.

An effective refractive index n_(e) of the microstructure layer 081 isshown by the following expression (5):n _(c) ={ff×n _(m) ²+(1−ff)}^(1/2)  (5)

where n_(m) represents a refractive index of a material forming themicrostructure, and ff represents a volume filling rate (filling factor)of the microstructure. This method for calculating the effectiverefractive index n_(e) is called as a first-order effective refractiveindex method, and it is the easiest method for converting themicrostructure (microstructure layer 081) into the effective refractiveindex.

On the other hand, the effective refractive index of the microstructurelayer 081 changes depending on a pitch and a three-dimensional shape ofthe microstructure. For instance, in a case where n_(m) is 2.3 and ff is0.5, the effective refractive index n_(e) calculated by the expression(5) is about 1.77. In contrast thereto, when an analysis is made byusing a rigorous coupled wave analysis (RCWA) method on an assumptionthat the pitch of the microstructure changes from 80 nm to 150 nm, theeffective refractive index n_(e) changes from 1.73 to 1.79. Therefore,it is difficult to calculate the effective refractive index accuratelyfrom only a cross-sectional shape and ff of the microstructure.

Thus, each embodiment calculates change of the effective refractiveindex of the microstructure layer (graded layer) 081 with respect to itsoptical film thickness. Spectral ellipsometry is used as one of methodsfor calculating the effect refractive index. The spectral ellipsometryis a method in which irradiations of linearly polarized lights ofmutually different wavelengths onto a specimen are performed to measurea ratio of polarized reflectances and a phase delay amount, and then arefractive index and film thickness model closest to the measurementresults is calculated. This method makes it possible to confirm whetheror not the microstructure satisfies the condition of the expression (2)even if details of the microstructure are unclear. If the expression (2)is satisfied, the graded layer may be a thin film layer and may be amicrostructure layer.

Further, methods for obtaining the graded layer of each embodimentinclude a method in which a comparatively sparse film formed uniformlyis soaked in a transparent sol-gel solution for a long time and then thesoaked film is sintered, and a method in which, during film formation bya binary film forming method, a mixture ratio is gradually changed. Ifthe graded layer satisfies the above-described refractive indexconditions, the graded layer can be produced by any manufacturingprocess.

An optical element on which the above-described graded layer is formedcan be used for various optical apparatuses. FIG. 23 shows a digitalcamera that is an optical apparatus using the optical element of eachembodiment.

Reference numeral 20 denotes a camera body, and reference numeral 21denotes an image-pickup optical system including a lens that is theoptical element of each embodiment. The image-pickup optical system 21includes plural lenses, and at least one thereof may be the opticalelement of each embodiment. Reference numeral 22 denotes a solid-stateimage pickup element (photoelectric conversion element) such as a CCDsensor or a CMOS sensor which receives an object image formed by theimage-pickup optical system 21, the solid-state image-pickup element 22being provided in a camera body 20. The solid-state image-pickup element22 photoelectrically converts the object image to generate imageinformation corresponding to the object image.

Reference numeral 23 denotes a memory that records therein the imageinformation. Reference numeral 24 denotes an electronic viewfinderconstituted by a liquid crystal display panel and the like, whichenables observation of the image information (that is, the objectimage).

The image-pickup optical system thus constituted using the opticalelement of each embodiment can realize a camera that suppressesunnecessary reflection in the image-pickup optical system and therebyhas high optical performance.

The optical element of each embodiment may also be used for a viewfinderoptical system of a camera, an illumination optical system of a liquidcrystal projector, a projection optical system thereof, and the like.The optical element having the above-described anti-reflection structurecan sufficiently increase an amount of light being transmitted throughthe optical element and can well suppress generation of ghost or flaredue to unnecessary reflection.

Hereinafter, Embodiments (simulation examples) 1 to 6 and ComparativeExamples 1 to 3 will be described.

Embodiment 1

In Embodiment 1, S-BSM14 (glass) made by OHARA Co., Ltd was used as abase member. The refractive index thereof for the wavelength 650 nm was1.6033. A graded layer having a refractive index structure shown in FIG.9 was formed on the base member. n_(s) was 1.530, n_(i) was 1.0, andt_(i) was 350 nm.

From the expression (1), n_(t) was 1.053, and the value of theexpression (2) was 0.72. FIG. 10 shows the reflectance characteristic ofEmbodiment 1. The reflectance characteristic included two minimumvalues, and a low reflectance of 0.2% or less was achieved in the entirevisible wavelength range.

Embodiment 2

In Embodiment 2, S-BSM14 made by OHARA Co., Ltd was used as a basemember. The refractive index thereof for the wavelength 550 nm was1.6088. An optical interference layer (refractive index: 1.50 andoptical film thickness: 113 nm) was formed on the base member, andfurther a graded layer having a refractive index structure shown in FIG.11 was formed on a surface of the base member. FIG. 12 shows therefractive index structure of the optical element of Embodiment 2. Partwhere the optical film thickness is negative shows the refractive indexof the base member. n_(s) was 1.38, n_(i) was 1.0, and t_(i) was 485 nm.

From the expression (1), n_(t) was 1.038, and the value of theexpression (2) was 0.50. FIG. 13 shows the reflectance characteristic ofEmbodiment 2. The reflectance characteristic included two minimumvalues, and a low reflectance of 0.1% or less was achieved in the entirevisible wavelength range.

Embodiment 3

In Embodiment 3, S-LAH55 (glass) made by OHARA Co., Ltd was used as abase member. The refractive index thereof for the wavelength 550 nm was1.8390. An optical interference layer (refractive index: 1.56 andoptical film thickness: 105 nm) was formed on the base member, andfurther a graded layer having a refractive index structure shown in FIG.14 was formed on a surface of the base member. The graded layer wasformed as a microstructure layer by first forming a thin film consistingprimarily of aluminum oxide by a sol-gel method and then hydrothermallytreating the thin film. This microstructure layer was analyzed withspectral ellipsometry. FIG. 15 shows the refractive index structure ofthe optical element of Embodiment 3. Part where the optical filmthickness is negative shows the refractive index of the base member.n_(s) was 1.39, n_(i) was 1.0, and t_(i) was 250 nm.

From the expression (1), n_(t) was 1.039, and the value of theexpression (2) was 0.53. FIG. 16 shows the reflectance characteristic ofEmbodiment 3. A low reflectance of 0.4% or less was achieved in theentire visible wavelength range.

Embodiment 4

In Embodiment 4, S-BSM14 made by OHARA Co., Ltd was used as a basemember. The refractive index thereof for the wavelength 650 nm was1.6033. A graded layer having a refractive index structure shown in FIG.17 was formed on the base member. n_(s) was 1.530, n_(i) was 1.0, andt_(i) was 350 nm.

From the expression (1), n_(t) was 1.053, and the value of theexpression (2) was 0.51. FIG. 18 shows the reflectance characteristic ofEmbodiment 4. The reflectance characteristic included two minimumvalues, and a low reflectance of 0.4% or less was achieved in the entirevisible wavelength range.

Embodiment 5

In Embodiment 5, S-BSM14 made by OHARA Co., Ltd was used as a basemember. The refractive index thereof for the wavelength 650 nm was1.6033. A graded layer having a refractive index structure shown in FIG.24 was formed on the base member. n_(s) was 1.530, n_(i) was 1.0, andt_(i) was 350 nm.

From the expression (1), n_(t) was 1.053, and the value of theexpression (2) was 0.78. FIG. 25 shows the reflectance characteristic ofEmbodiment 5. The reflectance characteristic included two minimumvalues, and a low reflectance of 0.5% or less was achieved in the entirevisible wavelength range.

Embodiment 6

In Embodiment 6, S-BSM14 made by OHARA Co., Ltd was used as a basemember. The refractive index thereof for the wavelength 650 nm was1.6033. A graded layer having a refractive index structure shown in FIG.26 was formed on the base member. n_(s) was 1.530, n_(i) was 1.0, andt_(i) was 500 nm.

From the expression (1), n_(t) was 1.053, and the value of theexpression (2) was 0.51. FIG. 27 shows the reflectance characteristic ofEmbodiment 6. The reflectance characteristic included two minimumvalues, and a low reflectance of 0.4% or less was achieved in the entirevisible wavelength range.

Comparative Example 1

In Comparative Example 1, S-BSM14 made by OHARA Co., Ltd was used as abase member. The refractive index thereof for the wavelength 550 nm was1.6088. A graded layer having a refractive index structure shown in FIG.19 was formed on the base member. n_(s) was 1.51, n_(i) was 1.0, andt_(i) was 440 nm. The graded layer shown in FIG. 19 was formed into afilm whose refractive index linearly changes with respect to itsphysical film thickness.

From the expression (1), n_(t) was 1.051. The value of the expression(2) was 1.19, which does not satisfy the condition of the expression(2). FIG. 20 shows the reflectance characteristic of ComparativeExample 1. Comparative Example 1 is inferior in the broadbandcharacteristic as compared with Embodiment 1.

Comparative Example 2

In Comparative Example 2, S-BSM14 made by OHARA Co., Ltd was used as abase member. The refractive index thereof for the wavelength 650 nm was1.6033. A graded layer having a refractive index structure shown in FIG.21 was formed on the base member. n_(s) was 1.53, n_(i) was 1.0, andt_(i) was 350 nm.

From the expression (1), n_(t) was 1.053. The value of the expression(2) was 0.48, which does not satisfy the condition of the expression(2). FIG. 22 shows the reflectance characteristic of Comparative Example2. Comparative Example 2 shows that its reflectance characteristicgreatly changes as compared with Embodiment 1 even though the opticalfilm thickness of Comparative Example 2 is equal to that of Embodiment1.

Comparative Example 3

In Comparative Example 3, S-BSM14 made by OHARA Co., Ltd was used as abase member. The refractive index thereof for the wavelength 650 nm was1.6033. A graded layer having a refractive index structure shown in FIG.28 was formed on the base member. n_(s) was 1.53, n_(i) was 1.0, andt_(i) was 500 nm.

From the expression (1), n_(t) was 1.053. The value of the expression(2) was 0.48, which does not satisfy the condition of the expression(2). FIG. 29 shows the reflectance characteristic of Comparative Example3. Comparative Example 3 shows that its reflectance characteristicgreatly changes as compared with Embodiment 1 even though the opticalfilm thickness of Comparative Example 3 is equal to that of Embodiment1.

Table 1 collectively shows numerical values of Embodiments 1 to 6, andTable 2 collectively shows numerical values of Comparative Examples 1 to3.

TABLE 1 EMBODIMENT EMBODIMENT EMBODIMENT EMBODIMENT EMBODIMENTEMBODIMENT 1 2 3 4 5 6 GRADED n_(s) 1.530 1.380 1.390 1.530 1.530 1.530LAYER n_(i) 1.000 1.000 1.000 1.000 1.000 1.000 t_(i) [nm] 350 485 250350 350 500 OPTICAL REFRACTIVE — 1.500 1.560 — — — INTERFERENCE INDEXLAYER OPTICAL — 113 105 — — — FILM THICKNESS [nm] BASE GLASS S-BSM14S-BSM14 S-LAH55 S-BSM14 S-BSM14 S-BSM14 MEMBER REFRACTIVE 1.6033 1.60881.8390 1.6033 1.6033 1.6033 INDEX λ [nm] 650 550 550 650 650 650 n_(t)1.05 1.04 1.04 1.05 1.05 1.05 t (n_(t)) [nm] 304 262 205 304 349 428 λ0.47λ 0.48λ 0.37λ 0.47λ 0.54λ 0.66λ n {t (n_(t))} 1.25 1.15 1.16 1.221.26 1.22 CONDITION (2) 0.72 0.50 0.53 0.51 0.78 0.51

TABLE 2 COMPARATIVE COMPARATIVE COMPARATIVE EXAMPLE 1 EXAMPLE 2 EXAMPLE3 GRADED n_(s) 1.511 1.530 1.530 LAYER n_(i) 1.000 1.000 1.000 t_(i)[nm] 440 350 500 OPTICAL REFRACTIVE INDEX — — — INTERFERENCE OPTICALFILM THICKNESS [nm] — — — LAYER BASE GLASS S-BSM14 S-BSM14 S-BSM14MEMBER REFRACTIVE INDEX 1.6088 1.6033 1.6033 λ [nm] 550 650 650 n_(t)1.05 1.05 1.05 t (n_(t)) [nm] 201 308 370 λ 0.36λ 0.47λ 0.57λ n{t(n_(t))} 1.30 1.20 1.20 CONDITION (2) 1.19 0.48 0.48

While the present invention has been described with reference toexemplary embodiments, it is to be understood that the invention is notlimited to the disclosed exemplary embodiments. The scope of thefollowing claims is to be accorded the broadest interpretation so as toencompass all modifications, equivalent structures and functions.

This application claims the benefit of Japanese Patent Application No.2008-222900, filed on Aug. 29, 2008, which is hereby incorporated byreference herein in its entirety.

1. An optical element comprising: a base member; and a first layer whichis formed on the base member and whose refractive index for a centraluse wavelength λ changes in a direction of a thickness of the firstlayer by 0.05 or more, wherein the first layer has an anti-reflectionfunction and satisfies the following conditions:n_(t) = n_(i) + 0.1 ⋅ (n_(s) − n_(i))$0.5 \leq \frac{{n\left\{ {{t\left( n_{t} \right)}/2} \right\}} - n_{t}}{n_{s} - {n\left\{ {{t\left( n_{t} \right)}/2} \right\}}} \leq 0.8$$\frac{\lambda}{4} \leq {t\left( n_{t} \right)} \leq {2\lambda}$1.0 ≤ n_(i) ≤ 1.1 where n_(i) represents a refractive index of a mostlight entrance side part of the first layer for the central usewavelength, n_(s) represents a refractive index of a most base memberside part of the first layer for the central use wavelength, t(n_(t))represents an optical film thickness of the first layer at which therefractive index thereof for the central use wavelength is n_(t), andn{t(n_(t))/2} represents a refractive index of the first layer for thecentral use wavelength at a position where the optical film thickness ist(n_(t))/2.
 2. The optical element according to claim 1, wherein atleast one optical interference layer is formed between the base memberand the first layer.
 3. The optical element according to claim 2,wherein a refractive index of at least one of the optical interferencelayer for the central use wavelength is between a refractive index ofthe base member and n_(s).
 4. The optical element according to claim 1,wherein the refractive index of the first layer changes more gently on alight entrance side than on a base member side.
 5. The optical elementaccording to claim 1, wherein the first layer is formed by pluralstructure portions each smaller than the central use wavelength.
 6. Anoptical apparatus comprising: an optical element which comprises: a basemember; and a first layer which is formed on the base member and whoserefractive index for a central use wavelength λ changes in a directionof a thickness of the first layer by 0.05 or more, wherein the firstlayer has an anti-reflection function and satisfies the followingconditions: n_(t) = n_(i) + 0.1 ⋅ (n_(s) − n_(i))$0.5 \leq \frac{{n\left\{ {{t\left( n_{t} \right)}/2} \right\}} - n_{t}}{n_{s} - {n\left\{ {{t\left( n_{t} \right)}/2} \right\}}} \leq 0.8$$\frac{\lambda}{4} \leq {t\left( n_{t} \right)} \leq {2\lambda}$1.0 ≤ n_(i) ≤ 1.1 where n_(i) represents a refractive index of a mostlight entrance side part of the first layer for the central usewavelength, n_(s) represents a refractive index of a most base memberside part of the first layer for the central use wavelength, t(n_(t))represents an optical film thickness of the first layer at which therefractive index thereof for the central use wavelength is n_(t), andn{t(n_(t))/2} represents a refractive index of the first layer for thecentral use wavelength at a position where the optical film thickness ist(n_(t))/2.